Wiktionary gives us the following etymology of amare.
Probably from Proto-Indo-European *am-a-, *am- (“mother, aunt”), a lost nursery-word of the papa-type. Compare amita (“aunt”), Old High German amma (“nurse”). Alternatively, O. Hackstein suggests Proto-Indo-European *h₂emh₃- (“seize”).
There's a fascinating conjecture in this etymology that amare comes from a nursery word meaning "mother" or "aunt", which I take to be a babble word such as "ma-ma". But unfortunately, I do not find this theory in de Vaan's entry.
amo, -are 'to love' [v. I] (Naev.+) Derivatives: amascere 'to begin to love' (Naev.), amasius 'lover' (PL+); amicus friend' (Naev.+), 'friendly' [o/a] (PL+), arnica 'female friend' (Naev.+), inimlcus [adj. / m.] 'unfriendly; an enemy (P1.+), inimicitia 'enmity, ill will' (P1.+); amor 'sexual passion, love' (Naev.+).
Pit. *ama- 'to take, hold\ It. cognates: Marr. amatens 'they have received'.
PIE *h3mh3- to take hold of. IE cognates: Olr. namae 'enemy' (< *n-AjmAj-^«/-); Skt pr. amfsi, amanti 'to take hold of; swear', ama- [m.], OAv. §ma-9 YAv. ama- [m.] 'attacking power'; Gr. όμνυμι 'to swear' [aor. όμόσαι, fut. όμοΰμαι] , άνώμοτος 'not under oath'.
The Latin meaning has developed from 'to take the hand of > 'regard as a friend'. Pit. *ama- could reflect PIE *h3mh3- in front of a vowel, cf. Schrijver 1991: 318. Schrijver 1991: 398ff. argues that the stative meaning of amare and the presence of a derivative amor point to a stative verb *ama-e-. Its formation must then post-date Pit., since Marr. amatens is not likely to have a stative suffix *-e-3 and has the transitive meaning * receive' of the IE cognates. The form amasius, because of its s, seems to be dialectal; maybe it is the same suffix as CLat. -arius. The adjectival function of amicus is original; the suffix -icus might be decasuative from an ins. in *-/A; plus *-Ao- (parallel cases in Latin are pudicus 'chaste' and mendicus 'needy'). The PIE root is reconstructed with initial *h2- in LIV, but Gr. points to *h3-,
Bibl.: WH 1:40, EM 29, IEW 778, Rix 1999: 523-24, LIV *h2emh3-. -> amplus
De Vaan gives the PIE root *h3mh3- ("to take hold of") for its etymology. This could be consistent with a babble word, but there is no explicit mention.
Is there any plausibility behind the idea that amare comes from a nursery word meaning "mother"? If so, how probable is this conjecture? Is there a consensus?